Britannica
Sources used in this answer
How does rotoinversion combine rotation and inversion in a crystal?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
crystal
A crystal form of elemental sulfur. Sulfur has an atomic weight of about 32.06 atomic mass units (amu), which means that its molar mass is 32.06 grams.
In crystallography, a rotoinversion is a compound symmetry element that combines a rotation about an axis with an inversion through a central point.12
During this process, the crystal is rotated by a specific angle—typically 360° divided by n—and then every atom is moved through a center of inversion to a new position. The resulting configuration must be identical to the crystal's original appearance for the symmetry to be present.12
Rotoinversion axes are categorized by the value of n (1, 2, 3, 4, or 6), which denotes the order of the operation:12
- 1: Equivalent to a simple center of inversion.2
- 2: Equivalent to a mirror plane.2
- 3: Equivalent to a threefold rotation axis combined with a center of inversion.2
- 4: Characterized by two top faces with identical faces inverted underneath.2
- 6: Equivalent to a threefold rotation axis with a mirror plane perpendicular to that axis.2
These elements are fundamental to defining the 32 point groups that classify the internal atomic arrangements and external morphology of crystals.12